Regarding the potential practical use of these confidence sets
in GAN applications, recall from the Introduction that when
\((\gamma _{0},\delta _{0})\in \Theta _{0}\) , the generator \(G(Z,\gamma _{0})\) 
gives the researcher a mechanism to produce synthetic data. In recent
work, [1]} have considered the
effect of small variations in the input noise on the synthetic images
produced. Similarly, one could consider how the produced images (or,
more generally, the distribution of \(G(Z,\gamma _{0})\) ) change when
the generator parameters vary within a certain confidence set.
Exploring the effect of such variations on the synthetic data produced
in other GAN applications
(such as DNA sequences, art, or music) would also be interesting.
We leave these issues for future research.
